Italian managers have been heading the betting to take over from Brian McDermott, who left Leeds by mutual consent on Friday.
Former Middlesbrough player Gianluca Festa was installed as favourite to get the job, with ex-AC Milan manager Massimo Allegri next in the running.
But Cellino insists he is not looking for an Italian manager to take the club forward.
"I have always said I wanted a British coach for this club," the 57-year-old told Sky Sports. "I am a man of my word and that is still the case.
"I am meeting three British coaches for talks on Saturday and want to get someone in place soon."
The Italian reiterated that he wanted a coach rather than a manager to replace McDermott.
"I want someone to take care of the preparation of the team, the training, the tactics and so on," he said. "Not the recruitment or the contracts, which I will take care of. The job is a coach, not a manager, which is an important difference."
Cellino called the club's players and coaches back to Elland Road on Monday - a month before they had been due back for pre-season - and says he was buoyed by the meeting.
"I spoke to each player, one by one, and looked each one in the eye," he said. "They were good meetings and I was impressed with the players.
"I think we can pull together and have a good season. This is about Leeds United, not Massimo Cellino."
Meanwhile, the Italian says he has agreed a deal to sell Cagliari to former Inter Milan board member Tommaso Giulini and that the sale is imminent.
A deal to sell to an American investment group led by the Italian Luca Silvestrone fell through.
"The Americans were messing about too long," Cellino revealed. "They wanted another 90 days.
"I have agreed to sell to Giulini and it should be finalised very soon. I wish them well. My heart is with Leeds now and all my work and energy is going into them."